You can probably find out what it is with the device IDs. In Device Manager, open the preferences of you Unknown Device and go to the "Details" tab. In the dropdown menu, choose "Device Instance ID". This will show at least one string like this:
It might not be complete (because the device is unknown, the Device Class (like "HDAUDIO" in my example), but you'll at least have the string after VEN_ and the one after DEV_. Write those down. The first is the Vendor ID and the second is Device ID (it's not vendor-specific to my knowledge, so you can use it on its own).
Now go to a site like PCI Database and search for the Device ID in the appropriate field. That sould return the device name. If there's more on the list, do a second search with the vendor ID. With that, you should be able to look for the proper drivers.